NECESSARY AND SUFFICIENT CONDITIONS FOR EXPANSIONS OF GABOR TYPE  

作　　者：Kunchuan Wang 

机构地区：[1]Tzu-Chi College of Technology, Taiwan

出　　处：《Analysis in Theory and Applications》2006年第2期155-171,共17页分析理论与应用（英文刊）

基　　金：This work is partially financed by NSC under 87-2115-M277-001.

摘　　要：In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.

关 键 词：Balian-Low theorem bi-orthogonal expansion orthogonal expansion Gabor expansion wavelet 

分 类 号：O17[理学—数学]